Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to
the range of traits or characteristics across a population, where for cells this could be the …
the range of traits or characteristics across a population, where for cells this could be the …
A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system
A cross-diffusion system with Lotka-Volterra reaction terms in a bounded domain with no-flux
boundary conditions is analyzed. The system is a nonlocal regularization of a generalized …
boundary conditions is analyzed. The system is a nonlocal regularization of a generalized …
Mechanics of finite nonlinear viscoelastic growth for soft biological tissues
Many soft biological tissues have a kind of rubbery properties and behave viscoelastic. The
main difference between soft biological tissues and rubber-like materials is that they can …
main difference between soft biological tissues and rubber-like materials is that they can …
From Finite to Continuous Phenotypes in (Visco-) Elastic Tissue Growth Models
In this study, we explore a mathematical model for tissue growth focusing on the interplay
between multiple cell subpopulations with distinct phenotypic characteristics. The model …
between multiple cell subpopulations with distinct phenotypic characteristics. The model …
On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure
Several recent papers have addressed modelling of the tissue growth by the multi-phase
models where the velocity is related to the pressure by one of the physical laws (Stoke's …
models where the velocity is related to the pressure by one of the physical laws (Stoke's …
Nonlocal-to-local convergence of the Cahn-Hilliard equation with degenerate mobility and the Flory-Huggins potential
The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its
rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link …
rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link …
Spatial segregation across travelling fronts in individual-based and continuum models for the growth of heterogeneous cell populations
We consider a partial differential equation model for the growth of heterogeneous cell
populations subdivided into multiple distinct discrete phenotypes. In this model, cells …
populations subdivided into multiple distinct discrete phenotypes. In this model, cells …
Nonlocal approximation of an anisotropic cross-diffusion system
T Dębiec, M Schmidtchen - arxiv preprint arxiv:2412.20188, 2024 - arxiv.org
Localisation limits and nonlocal approximations of degenerate parabolic systems have
experienced a renaissance in recent years. However, only few results cover anisotropic …
experienced a renaissance in recent years. However, only few results cover anisotropic …
Gradient Flow Solutions For Porous Medium Equations with Nonlocal L\'{e} vy-type Pressure
We study a porous medium-type equation whose pressure is given by a nonlocal L\'{e} vy
operator associated to a symmetric jump L\'{e} vy kernel. The class of nonlocal operators …
operator associated to a symmetric jump L\'{e} vy kernel. The class of nonlocal operators …
Scaling limits for a population model with growth, division and cross-diffusion
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article
is to explore models through different scales for a spatial population of interacting, growing …
is to explore models through different scales for a spatial population of interacting, growing …